The Stability of Self-Shrinkers of Mean Curvature Flow in Higher Codimension
arXiv:1204.6116
Abstract
In this paper, we generalize Colding and Minicozzi's work \cite{CM} on the stability of self-shrinkers in the hypersurface case to higher co-dimensional cases. The first and second variation formulae of the -functional are derived and an equivalent condition to the stability in general codimension is found. Moreover, we show that the closed Lagrangian self-shrinkers given by Anciaux in \cite{An} are unstable.
We in the end of 2010, obtained the same foundation part of the article arXiv:1204.5010v1 by B. Andrews, H. Li and Y. Wei, entitled with "F-stability for self-shrinking solutions to mean curvature flow". In our article, we at the same time showed the unstability of Anciaux's closed Lagrangian self-shrinkers